Progress in Higher-Dimensional Field Theories

Abstract

It is a non-trivial issue to define higher-dimensional gauge theories at any energy scale since their interactions become stronger at high energies. In the presence of supersymmetry, it was argued that certain five-dimensional gauge theories make sense by showing the existence of their ultraviolet fixed points. An attempt of classifying supersymmetric five-dimensional gauge theories had been performed both from quantum field theory and string theory but there was inconsistency between the two approaches. Recently, the inconsistency has been resolved and a lot of new five-dimensional supersymmetric gauge theories which have ultraviolet fixed points have been discovered. In this article, we review such progress in five-dimensional supersymmetric gauge theories. We also comment on applications of string theory to compute various physical quantities of five-dimensional gauge theories.